DIFFERENTIABLE AND COMPLEX DYNAMICS OF SEVERAL VARIABLES by Pei-Chu Hu, Chung-Chun Yang ( 9789048152469 )

Item Details

Title:

DIFFERENTIABLE AND COMPLEX DYNAMICS OF SEVERAL VARIABLES

By:

Format:

Paperback

List price:	£90.00
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ISBN 10:

9048152461

ISBN 13:

9789048152469

Publisher:

SPRINGER

Pub. date:

5 December, 2010

Edition:

Softcover reprint of hardcover 1st ed. 1999

Series:

Mathematics and Its Applications 483

Pages:

342

Synopsis:

The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.

Illustrations:

X, 342 p.

Publication:

Netherlands

Imprint:

Springer

Returns:

Returnable

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DIFFERENTIABLE AND COMPLEX DYNAMICS OF SEVERAL VARIABLES (HB)